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On free boundary problems in two dimensions |
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| Authors: | Hans Lewy Tang Zhiyuan |
| Affiliation: | 1. Departments of Mathematics, University of California, 94720, Berkeley, California 2. Department of Mathematics, University of California, Berkeley, California 3. Chengdu, China |
| Abstract: | Let L be a linear elliptic operator in two dimensions with analytic coefficients and of second order, andu(x, y) a solution of Lu=0 in a simply connected domain ω with rectifiable boundary Γ. Suppose ψ(x, y) analytic on ω∪Γ and L ψ≠0 there.H is shown that ifu and ψ coincide with first derivatives on an open portion Γ0 of Γ, then Γ0 permits the representation λ=x (θ),y=y (θ) withx(θ),y(θ)analytic functions of a real parameter θ. |
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